In [1]} the authors studied the recovery of a compact Finsler manifold from its boundary distance data. In contrast to earlier Riemannian results [2]}, [3]} the data only determines the topological and smooth structures, but not the global geometry. The Finsler function \(F\colon TM \rightarrow [0,\infty )\)  can be however recovered in a closure of the set \(G(M,F)\subset TM\) , that consists of points \((p,v)\in TM\)  such that the corresponding geodesic \(\gamma _{p,v}\)  is distance minimizing to the terminal boundary point. They also showed that if the set \(TM \setminus G(M,F)\)  is non-empty then any small perturbation of \(F\)  in this set leads to a Finsler metric whose boundary distance data agrees with the one of \(F\) . If \(G(M,F)=TM\) , then the boundary distance data determines \((M,F)\)  up to a Finsler isometry. For instance the isometry class of any simple Finsler manifold is determined by this data.
The same is not true if only the boundary distance function is known [4]}. Thus a simple Finsler manifold is never boundary rigid. In [5]} the main result of [1]} was utilized to generalize the result of [7]}, about the broken geodesic data, on reversible Finsler manifolds, satisfying a convex foliation condition.
